stat251 fall06 midterm1

# stat251 fall06 midterm1 - Midterm Exam 111 Stat 251 Fall...

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Unformatted text preview: Midterm Exam 111‘ Stat 251 Fall 2006 it i \xnlame_ OC‘i‘ m {mob TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Answer the question True or False. 1) ln skewed distributions, the mean is less affected by extreme observations than the median. 1) E * 2) The mean of a discrete random variable must be one of the values in which the random variable 2) F can result. 3) If A and B are independent events, then A and B are mutually exclusive also. 3) F MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 6 ,5 4) The top speeds for a sample of fiVe new automobile brands are listed below. Calculate the standard 4) I; 141:8 deviation of the speeds. S 1 :M W : 50‘"1 5 6—79—1353: = \Sta. 2 5‘ Gm. 345?: wens 1 \ 190,100,120,135,180 W ‘ = QM"? g a as 1:44 2 “ 19 s z -. is; A) 166.5683 B) 100.00 C) 232.5134 @387298 3 { {ST 7 a? (1 m \A‘HORT ANSWER. "4' w r r w ,»..,, i 5) A local newspaper claims that 70% of the items advertised in its classified advertisement 5) . l :10: I : 0.7 section are sold within week of the first appearance of the ad. To check the validity of the claim, the newspaper randomly selected n = 25 advertisements from last year's classified ~ 4; I; '1 t 0'5 advertisements and contacted the people who placed the ads. They found that 16 of the 25. H = 2—5 items sold within a week. Based on the newspaper's claim, is it likely to observe 16 or less )( = Ho people who sold their item within a week; 4 I p 0019) with“ = m)‘ (a) = o .. l3%b a on» *M&W%Wtﬂﬁb m523=32\$mﬂxn\wm% 6) Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class had a mean of 69 with a standard deviation of 3.7. Suppose a student 4 gets a 76 on the history test and a _6_Z on the physics test. On which test did the student perform better relative to the class performance? What is your evidence of this? Note: To obtain credit for this question, there must be clear evidence offered. Guessing won't get it théjlltll images—b W‘th S - 0.9+ He did betttr m 306'th — WWW W3. Stove 0:03 A " l qs.’ ' mesa-t it. he \‘y‘it’a .~-. l l NWT if m “3% i 3 , . 4i9l5 t0? .taw s fi‘lgra lo Wit ‘i‘l “t We 6’5: ﬂ . MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 7) A study was recently done that emphasized the problem we all face with drinking and driving. 7) a Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were v the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below: Number of Vehicles Involved Did Alcohol Play a Role? What proportion of the accidents involved more than a single vehicle? A) 44/400 B) 18/400 @16/400 D) 84/400 I: amma Temte bakes six pies a day that cost \$2 each to produce. On 23% of the days she sells only E 2 8 2’5 '1 two pies. On 10% of the days, she sells 4 pies, and on the remaining 67% of the days, she sells all six 093:“ 1“ “cs 1 pies. If Mama Temte sells her pies for \$5 each, what is her expected rofit (revenue—cost) for a day's ‘ .. 4; ‘ _ ‘2 :voithtgf pies? [I‘llntfioAleZme that any leftover pies are givSen away. ( .2 39L “ﬁg (01 E c, O I O) S4}. ) ’ IZ3 ' n > "ﬁ P(P\r> y «/ qxg=¢20-i1=3© *JO: Qv‘b ‘13 .Ltta AAA": 4.?8X52 té:)’5€'|2“ tz%¥.bﬁ= “30H LI "5’ '.‘+ ~24\$ (0 t u - to 1 . 1 A) —\$7.00 @2440 C) —\$7.12 D) \$12.40 12 n+0 9) The breakdown of workers in a particular state according to their political affiliation and type of 9) B job held is shown here. Suppose a worker is selected at random within the state and the worker's v political affiliation and type of job are noted. Political Affil'ation Independent mm 13% L3 = o 37:42: 2e Republican 11% White collar Type of job Blue Collar Given the worker is a Democrat, what is the probability that the worker is in a white collar job.) A) 0.52 @1385 C) 0.2 D) 0.294 10) The peak shopping time at home improvement store is between 8:00—11:00 am on Saturday 10) A mornings. Management, at the home improvement store, randomly selected 190 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items each of the customers purchased, as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store. @umber of items — discrete; total time — continuous -B)-number.of items — discrete; total time - discrete C) number of items — continuous; total time - discrete D) number of items — continuous; total time — continuous 11) A stateenergy agency mailed questionnaires on energy conservation to 1,000 homeowners in the 11) state capital. Five hundred questionnaires were returned. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: A: [The home is constructed of brick}'—‘ B: [The home is more than 30 years old] C: {The home is heated with oil] In terms of A, B, and C, describe a home that is constructed of brick and is less than or equal to 30 years old. A)(AnB)C AnBC C)AuB D)AnB 12) The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor 12) k of a company's success has been proven time and again to be customer service. A study was conducted to study the customer satisfaction levels for one overnight shipping business. In addition to the customer's satisfaction level, the customers were asked how often they used overnight shipping. The results are shown below in the following table: Satisfaction level Medium Frequency of Use riaﬁrmqntbmr 2 35 per month \ > 5 per month“ A TOTAL High A customer is chosen at random. Given that the customer uses the company two to five times per month, what is the probability that they expressed medium satisfaction with the company? @55/200 B) 55/220 C) 55/700 D) 365/700 13) The output below computed the mean and median for the national dropout rates for high school 13) students in 1998 and 2002. Drop 1998 Drop 2002 N 51 51 MEAN 28.32 26.38 MEDIAN 27.98 25.64 Interpret the 2002 median dropout rate of 25.64. ~A+The average dropout rate of the 51 states was 25.64%. MQaYi ~—B«)—The most frequently observed dropout rate of the 51 states was 25.64%. mOd ( ﬁ-H'alf of the 51 states had a dropout rate of 25.64%. alf of the 51 states had a dropout rate below 25.64%. mu m h‘ av)on B—3 14) The random variable x represents the number of tests that a patient entering a hospital will have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. 62=§1(>17l/\)1'?”)3 2-J=\,S‘D‘b ‘ " 1' r” ‘1 (0 » ‘1»!le fl— 3’. \ A) mean: 3.72; standard deviation: 2.52 @nean: 1.59; standard deviation: 1.09 B) mean: 2.52; standard deviation: 1.93 D) mean: 1.59; standard deviation: 3.72 15) Suppose a basketball player is an excellent free throw shooter and makes 93% of his free throws "(i.e., he has a 93% chance of making a single free throw). Assume that free throw shots are indgpggdent of one another. Suppose this player gets to shoot three free throws. Find the probability that he misses all three consecutive free throws. 1.490415%.0221 (. my .o’MM) C 14) (were): .4003 .’ 6=W‘W =\.o<b7 >752} l-(oxoaasv) , ,. = o. ' ‘ 093044557 y= 5.tt9,x\or“" 1616b ‘ '-= . 30?, 2, #9908044 @0003 ~ Ciyti9997q @01956 '16) Consider the given discrete probability distribution when answering the following question. Find the probability that x equals 5. - . i—(o.2=sro.0\ro.oco)=o.b<b x 3 5 6 9 P(x) 0.23 ? 0.01 0.08 A) 3.4 @168 C) 0.32 D) 1.6 17) At the US. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 116 mph and 124 mph? A) 0.997 B) 124 (if. .047 44,7 4 W gill“) . 5, 0 W // 0‘97/7750; a ‘55 l" 3—4 B 16) saw \I ...
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